Final answer:
The equation for the relation E = {(x, y): (2, 15), (5, 30), (8, 45), ...} in the form y = mx + b is y = 5x + 5. The slope m is 5, calculated from the given points, and the y-intercept b is 5, determined by substituting one point into the equation and solving for b.
Step-by-step explanation:
To write the equation for the relation E = {(x, y): (2, 15), (5, 30), (8, 45), ...} in the form y = mx + b, we first need to determine the slope, m, and the y-intercept, b. The slope can be found by taking two points from the set and dividing the difference in y-values by the difference in x-values, also known as the rise over run. Using the points (2, 15) and (5, 30), we calculate the slope as m = (30 - 15) / (5 - 2) = 15 / 3 = 5.
Now that we have the slope, we use one of the given points to find the y-intercept. Plugging the point (2, 15) into the equation y = mx + b and replacing m with 5, we get 15 = 5(2) + b, which simplifies to 15 = 10 + b. Solving for b, we have b = 15 - 10 = 5.
Therefore, the equation of the line is y = 5x + 5, which represents the relationship between x and y for the given set of points.